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        <td class="header">&nbsp; Integer Interferogram Combination<br>
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<p>It is possible to stack several interferograms of the same site to increase their clarity or reduce the number of
    fringes, thus creating an integer interferogram combination (IIC) [R13]. The combined interferogram can
    have a better altitude of ambiguity <i>h<sub>a</sub></i> than any of the source interferograms.</p>

<p>After correction for topographic and orbital contributions,
    the interferogram contains three kinds of information: </p>


<ul>
    <li>The number of fringes <i>&#957;</i> representing noise due to thermal noise or to partial incoherence.</li>
    <li>The number of fringes <i>&#949;</i>/<i>h<sub>a</sub></i> due to the errors <i>&#949;</i> in the DEM,
        where <i>h<sub>a</sub></i> is the altitude of ambiguity.
    </li>
    <li>The number of fringes <i>&#956;</i> caused by any differential effects, including local variations in the
        atmospheric thickness, as well as local ground motion between the acquisition times.
    </li>
</ul>


<p>The interferogram in which the effects of topography and the 'orbital fringes' have been retrieved gives
    us the fractional part of:</p>
<div align="center"><img src="images/iic_eq1.png"></div>
<br>


<p>If we multiply the interferogram by an integer <i>q<sub>1</sub></i>, we will likewise
    multiply
    the number of phase transitions and the initial integer values. Note that the
    integer values remain unknown unless unwrapping has been performed. We obtain the
    fractional part of:</p>
<div align="center"><img src="images/iic_eq2.png"><br></div>


<p>If we combine the first interferogram with a second, characterised by another independent noise distribution,
    another altitude of ambiguity, other differential effects and another multiplication factor <i>q<sub>2</sub></i>,
    but the same local DEM error <i>&#949;</i> , we obtain the fractional part of:</p>
<div align="center"><img src="images/iic_eq3.png"><br></div>


<p>As a consequence of the multiplications, the RMS amplitude of the noise becomes:</p>
<div align="center"><img src="images/iic_eq4.png"></div>
<br>


<p>This resulting increase of the noise in practice limits the
    choice of the absolute value of <i>q<sub>1</sub></i>
    or <i>q<sub>2</sub></i> to less than 3.</p>

<p>The interferogram resulting from this kind of combination
    exhibits an equivalent altitude of ambiguity <i>h<sub>ae</sub></i>, written as:</p>
<div align="center"><img alt="" src="images/iic_eq5.png"></div>
<br>


<p>Phase unwrapping applies to altitudes of ambiguity lower than 100&#8211;200 m and greater than 10 m
    in interferometric conditions. Even choosing <i>q<sub>1</sub></i> and <i>q<sub>2</sub></i>
    to be 1, 2, or 3 allows us to reach an equivalent altitude of ambiguity of more than 100 m most of the time.
    Using this method, we create more interferometric combinations with a high altitude of ambiguity, as if we had
    a small orbital separation.</p>

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